Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation

Note 63. IIR Phase-Splitting Networks for Generating Analytic Signals

This note describes the design of IIR phase-splitting networks that can be used to generate complex-valued analytic output signals from real-valued bandpass input signals. Refer to Note 60 for a discussion of analytic signals and their properties.

The analytic associate, x_a[n], of a real bandpass signal, x[n], can be formed as

where P and Q are all-pass filters that together comprise a phase-splitting network such that the phase of Q lags the phase of P by 90 degrees for all positive frequencies, and the phase of Q leads the phase of P by 90 degrees for all negative frequencies. ...